Essays on Algebra

1. Introduction. Digital signal processing is a very mathematical subject so main mathematical ideas should be outlined to ensure a successful learning. 2. Algebra. Algebra is a systematic notation of quantitative relationship between expressions divided (or joint) by the sign ‘=’ and the collection of rules to manipulate such expressions and values (variables) they contain. 3. Functions, Numbers, and Graphs. Functions are used to denote relations (dependencies) between variables: if one variable depends on another, then the latter variable is called the independent variable, while the former is called the value of the function. If we use the horizontal axis ...

DeMorgan’s Theorem is one of the most important transformation rules in digital electronics. It is a pair of transformation rules which could be applied in propositional logic and are both valid for rules of inference. It was named after its developer Augustus De Morgan who is a British Mathematician. The simplest way to define DeMorgan’s Theorem is that the logical expressions remains unchanged when the inversion bar of the expression is broken and the operation is changed to its opposite. DeMorgan’s Theorem come about in order to simplify logical expressions in mathematics. It was influenced by ...

Communication is an activity, through which people give, receive, or exchange facts, ideas, needs, observations and feelings, intentionally or unintentionally through spoken words, drawings, signals, notes, and behavior. Communication is a social activity involves interaction of people either physically or through appropriate media. Apart from being continuous, it is vibrant, multifaceted and frequently changes. Defining communication is complex; many varying definitions exist with each person having a different version (West & Turner, 2007). Personally, communication is very important to the human nature because it affects all the facets of our day-to-day lives. We use communication to understand our environment and our lives ...

In this paper we summarize what’s written in the book “Elementary Linear Algebra” by Howard Anton & Chris Rortes. The book describes the basic methods of elementary linear algebra, linear nature of considering objects: vector (or linear) space, linear transformations, systems of linear equations, quadratic and bilinear forms. The main linear algebra tools considered in this book are systems of linear algebraic equations, determinants, matrixes, conjugation.

The book consists of ten chapters; each part describes one of the major areas of linear algebra.

The first chapter is “Systems of Linear Equations and Matrices”. A System of m linear algebraic equations with n unknown variables (or linear system, also used the abbreviation SLAE) ...

Abstract.

This paper explores a detailed plan to promote achievement and success among the sixth grade middle school students in the math discipline. It focuses on the decreased mastery of this discipline among this target group. Looking at possible ways to improve the mastery of maths subject among the sixth grade students, the paper identifies the characteristics of this population, and explains why the population is any target of discussion. It outlines the problems the group is experiencing in details, and establishes ideas, theories and practises that can promote achievement and success among the sixth grade students in the mathematics discipline. ...

Introduction

Security systems are undergoing development with the development of cryptographic protocols that help to secure these communications channels. There have been extensive researches that have been carried out to come up with better security mechanisms that will secure information systems. A cryptographic protocol is a protocol which makes use of cryptography so that they are able to achieve their goals, these goals could include sending private or public keys over the network. There are protocols that are used for securing security systems. This paper will focus on two protocols, NRL analyzer and Bellare-Rogaway model (Tanenbaum, 2003).

NRL analyzer

How it works

It ...

The purpose of the lesson, which was to prepare students for pre-algebra, was made clear by the teacher. However, as the lesson proceeded, the teacher explained that the students could use the pan-balance to replace objects with other variables. These variables could be used in working out uncomplicated algebraic expressions. The flow of the lesson deviates from the key purpose. This creates an element of contradiction from the initial purpose of the study. At the end of the lesson, the students had learnt on replacements other than understanding the key concepts of pan balance and pre-algebra.

The teacher is ...

Set theory is an essential language in learning mathematics, especially in algebra. Set theory, when is a prerequisite to algebra and other mathematical abstract concepts, it enhances their cognition. Dogan (2011) argues that cognitive difficulties in understanding abstract mathematical concepts results from the failure to master set theory language. Dogan (2011) found that set theory language is essential for proper response to linear algebra problems. Moreover, his study revealed that misconception of algebra and other abstract mathematical concepts was highly contributed by lack of mastery of set theory language. There are three elements of set theory that are critical in ...

Is being educated in all subjects necessary in every profession?

"You have to learn, young man. Philosophy. Theology. Literature. Poetry. Drama. History. Archeology. Anthropology. Mythology. Music. These are your tools as much as brush and pigment. You cannot be an artist until you are civilized. You cannot be civilized until you learn. To be civilized is to know where you belong in the continuum of your art and your world. To surmount the past, you must know the past." This particular statement by Mark Rothko to a budding artist from the play “Red” by John Logan notes that to be civilized, one must understand a variety of disciplines before he can ...

Abstract

The element of teacher bias in the education institutions is of great significance to the educational development of the students. It is important in the sense that it provides insights into the role of the integration of the students and the teachers for educational success. Research has been conducted to determine the potential effects of the teacher bias on the educational achievement of the students. This research encompassed both the qualitative and the quantitative methods in identifying these concepts. Classroom observations were conducted for the research and results drawn and analyzed from the data. The results of this research ...

Application of Algebra in computing

Algebraic principles are used extensively in computing. In computer science, the computer algebra is called algebraic computation or symbolic computation. This is used mainly in software development and the associated algorithms that are used in the manipulation of mathematical expressions and objects. Kaltofen Erich (1982) noted that the long-known algorithms that were being used proved to be very long and this necessitated the revisiting of classical algebra with the intention of making them effective and efficient. In specific terms, algebra is used in the following fields of computing. Encoding: in encoding, data that is arranged in arrays or ...

Before the onset of the seventeenth century, the Middle East had dominated in the area of mathematical ideas. Many philosophers and scientists came up with compelling ideas in mathematics and proved many formulas in mathematics from the Middle East. Essentially, there were distinct factors that influenced scholars and philosophers from this region to be competent in mathematics and other scientific inventions as they were. However, in the onset of the seventeenth century, Europe replaced the Middle East, which had been vastly associated with mathematical discoveries. Europe thus became the new engine house of mathematical ideas from the seventeenth century . ...

Instructional leader

Abstract This essay will discuss tools, which will assist the educational leader in promoting the learning outcome and assessment of students by guiding, encouraging, motivating and supporting the school culture and offering instructional programs in the area of mathematics, which are conducive to student learning and the professional growth of staff members. Mathematical tools are measured and structured to assist teachers who can examine distinct or various approaches to improve the mathematics performance of students in middle school. Students that are in elementary grades 3 through 9 accept the challenge and the desire to succeed. According to research, ...

CRITIQUE OF “THE ALGEBRA OF INFINITE JUSTICE”

The Algebra of infinite justice is an article written by Arundhati Roy. Arundhati was born on Novemeber 24, 1961 in Shillong to a Bengali Hindu father and a Christian mother. She won a Booker Prize for her first novel-The God of Small Things in 1997. After that she wrote on many topics on politics, nuclear weapons s in India, corruption among others. One of her writing is “The algebra of infinite justice” where she criticizes the role of USA in the beginning, propagation, and methods to fight terrorist. She claims the USA is created terrorist and is attempting to destroy them. She ...

Principal concept analysis may be defined as the statistical analysis tool relevant for the transformation of detailed or complex data into simple and easy to understand data. The method focuses on the use of principal components of statistics for possible interpretations. In most cases, the method does not include statistical assumptions. However, the method will always give extremely significant results for data that contains multivariate normal distribution. The data is extensively significant in determining the hypothetical variables or components that are extensively useful in the multidimensional data. In other words, the method PCA is a method significant in projecting one-dimensional ...

Mid-Term

Cope Bloom’s Taxonomy in Mathematics Teaching Bloom’s and Anderson’s Taxonomy This paper discusses a brief history and background of the original Bloom’s taxonomy established in 1956 and the revised Bloom’s taxonomy by Anderson et al. in 2002. It attempts to explore how the taxonomy of learning in the cognitive domain is applied in a specific teaching field such as Mathematics. In 1956, Benjamin Bloom headed a committee of educators to establish a systematic hierarchy in classifying educational objectives. They published their findings in a book, Taxonomy of Educational Objectives: The Classification of Educational Goals (Bloom ...

The Binary System is the simplest numeration of all positional number systems. The basic of this system is discovered by Gottfried Leibniz, who was also the co-creator of Calculus, in his work Explication de l'arithmétique binaire in 1679. In this work, he was trying to translate verbal statements into mathematical ones. Yi Jing, which was said to be created by the so-called Third millennium father of Chinese writing Fu Xi, depicts yin and yang. It was represented in binary, with yin as 0 and yang as 1, involving eight trigrams and sixty-four hexagrams. Leibniz’s works were ...

Education is by far the most important activity in a person’s lifetime. It is said that education never ends and a person’s capacity to learn is only limited to his or her belief of the knowledge they possess. Educational institutions all over the world impart knowledge to young minds in various fields established by human kind throughout its existence. However, education is not only about gaining knowledge and certifying oneself (Hacker). It is about increasing one’s awareness, one’s own personality and one’s one perspective of the world around them. However, each individual has a different take on ...

Introduction to Electrical Engineering

Electronic gadgets are in great demands today because of the evolution of high technology and advancement of internet connection. People are always finding something new, so, many companies are giving funds for research. With the help of electrical engineers, companies are providing new gadgets every now and then to surpass the features of the previous gadgets that they have been produced. In order for the students to solve complexities of a problem, electrical engineering program gives an opportunity to learn new things by experimentation and analytic solving. Therefore, this program mainly tackles mathematics and science. Because of experimentation and ...

<Author’s Name> <Institutional Affiliation> Wolfram Alpha is modern powerful search engines that caters various fields of studies launched in May 2009. The design of these engines initially concentrates on formula and algorithm growth in Mathematics as a result of extensive and sustained data gathering conducted by the team . In the field of mathematics, it provides supports on specific categories of topics such as mathematical functions, algebra, computational sciences, probability and statistics, calculus and analysis, geometry as well as discrete mathematics. Beyond the common mathematical functions, the team of Wolfram recently added Bessel functions, zeta ...

<Student’s name> <Professor’s name>

Introduction Euclid (near 365 - 300 BC) is a Greek mathematician, lived in Alexandria, in the 3rd BC. The main work "Elements" (15 books), containing the basics of ancient mathematics, elementary geometry, number theory, the general theory of relations and the method of determining areas and volumes, which included elements of the theory of limits, has had an enormous influence on the development of mathematics. He worked on astronomy, optics, music theory. Information about the time and place of his birth did not reach us, but we know that ...

There are several mathematical formulae that mathematicians and scientists have come up with over time. These mathematics formulae solve or address several issues or problems in the real world or mathematical and scientific field. One of the well-known mathematicians is Augustin Louis Cauchy. He is credited for coming up with the Cauchy sequence (the Cauchy sequence is named after him). This paper explores the Cauchy sequence, explaining its nature, form, application, and other related aspects of the sequence. What is Cauchy sequence? This is a sequence whose elements become arbitrarily close to each other in the course of progression ...

The fundamental theorem of algebra (FToA) is states that each non-constant single-variable polynomial with complex coefficients has at least one complex root. In fact, there are many equivalent formulations, such as this: every real polynomial can be represented as a product of real linear and real quadratic factors. Early studies equations by al-Khwarizmi (from 800) are devoted only to positive real roots and have no relation to the FToA. Cardano was the first to realize that it is possible to work with the values ​​more general than real numbers (Geuvers, Wiedijk & Zwanenburg, 2002). This discovery was made in the ...

Solving Real-World Problems Using Algebra.

A chain store manager has been told by the main office that daily profit, P, is related to the number of clerks working that day, x, according to the function P= -25x2+300x . What number of clerks will maximize the profit, and what is the maximum possible profit?

Solution

The Quadratic equation P= -25x2+300x can be modified to the form y= -25x2+300x, where P= y. Modifying the equation in this form enables us to plot the function y= -25x2+300x

For various values of x where x is a positive integer.

The general equation of a quadratic is given by y= ax2+bx+c where a, b and c are the ...

The article, “Predicting Human Brain Activity Associated with the Meanings of Nouns” was written by Tom M. Mitchel, Svetlana V. Shinkareva and their five associates. The article was published in Science in May 2008. It outlined a computational program that predicted which parts of the brain were stimulated and would respond to certain words and images, or certain stimuli. I found several concepts of the article very interesting. For example, the basis of the article’s studies was founded on creating a computational framework subject to linguistics. In layman terms, a grid of the mind was drawn up, based on nouns. Scientists ...

Aims

The main aim of the experiment was to verify the vector cross product and its torque. Other aims were to understand the mathematical model of carrying out the vector cross product and to determine the equilibrium in a system under torque.

Introduction

In the manipulation of vectors through multiplication two kind of products are achieved, the dot product and the cross product. The dot product of a vector is a scalar quantity and hence it only has magnitude. An example of scalar quantity is work done by a force. The cross product of a vector produces a quantity that has both direction and magnitude. ...

200 Years of Eastern and Western Medicine and Science

200 Years of Eastern and Western Medicine and Science – Comparison of Developments between 1800-1900 1 Introduction Thesis Statement: The period between 1800-1900 marked the evolution of Eastern and Western science and a significant cultural exchange that laid the foundation of modern day globalized science. The purpose of this paper is to trace the development of science and medicine across two centuries in both the East and the West. The timeframe that has been selected for the study extends across the 19th to the 20th century which is a very ...

Validity and Scope of Approximate Methods of Integration

Introduction Addition of discrete numbers is pretty straightforward; more than 80% of the human population can make mental calculations instantly. So when integration was introduced as a kind of addition in a continuous domain, I was not very worried. However, it didn’t take me long to realize that understanding integration is more than solving a bunch of problems using well defined techniques. So in my pursuit to understand the topic well, I decided to research upon how some of these techniques (Trapezium Rule and Simpson’s Rule) came about, how they work, and what they really mean. With this intent, ...

QUESTION 1

Function – A function is the relationship that exists between an input and output such that one input has only one possible output. This implies that a function takes an input and produces an output based on the input (Cheney & Kincaid, 2012).

Examples

Linear function y = 2 x

Quadratic function

y = 2 x2

Third degree polynomial

y = 2 x3

Exponential function

y = e2x

Logarithmic function

y = log 2 x

Periodic function

y = sin x Domain of a function - The domain of a function is the set of inputs for which the output of the function exists (Cheney & Kincaid, 2012).The domain of linear function is (- ∞ to ∞), quadratic function is (- ∞ to ∞), ...

Kirchhoff’s Laws are fundamental in the analysis of electrical and electronic circuits. They describe the behavior of linear circuits accurately, and work well with approximations in other types of systems as well, making them extremely useful (“Electrical Principles”, 2013). Further, they are more popular and widely used than Maxwell’s equations, from which they can be derived. This is because Maxwell’s equations are very complex and involve brute Mathematics to solve even simple circuits, while the Kirchhoff’s laws are relatively much easier to use in most cases.

There are two laws which were given by Kirchhoff:

1) Kirchhoff’s Current law (KCL) 2) Kirchhoff’ ...

Given Traffic Scenario

Figure 1: The intersections of five one-way streets 1) There are five streets making six intersections. All the streets are one-way, that is, cars can move along only one direction on any street. The number of cars between intersections is the taken to be the traffic flows. For optimal flows, it is assumed that the number of cars entering an intersection in a given time must equal the number of cars leaving that intersection in that time. Also the number of cars entering and leaving any street per unit time is as mentioned in Figure 1. It is important ...

The properties of real numbers is a fundamental concept of basic algebra. Any given individual should be aware of these concepts as we may face them in our everyday lives without even noticing. When you actually are doing simple math operations while buying groceries or calculating your monthly expenses, you are dealing with real numbers, and, therefore, you should be aware of their properties in order not to make a mistake in your calculations. The distributive law, simplification procedures and operations with removing parentheses are important to know anytime you are facing a problem which involves calculations. The knowledge of these properties ...

“An educated Petersburg, is a successful Petersburg”

Introduction Petersburg is an independent American city found in the Virginia state of the United States. Its population is overwhelmingly black with an estimated percentage of 79. The city has got a rich industrial history and once supported a booming tobacco industry. Petersburg boasts of several schools in all learning levels.

Overview of the campaign

Generally, Petersburg education standards are adversely reviewed in all quarters. This is a view well rooted in the collective mind of the nation. Recently, a study was conducted on the relationship of education standards and affluence. It was noted that poorer kids do worse than their richer counterparts. The population in ...

Mathematics and sciences gave me one of the biggest challenges in my early education life. Having studied in a private school in the US where I was introduced to Everyday Math, I realized that it was not as easy as the tutors would want us to believe. An s early as I can remember, the educators used old and ineffective teaching criteria. Having to count from 0 to 1000 and playing games seemed tedious at the moment but it was as much impractical as I would learn later on. Addition and subtraction facts were scanty, and less emphasized. Until 5th ...

A.1A single mom has to go back to work and needs day care for her baby. She is trying to decide between a baby sitter, who cares for children in her home,ora nearby day care center. The baby sitter charges a flat rate of $10 per hour, and the localday carecenter charges $325 per week, for 5 days per week, up to 40 hours. (Mon-Fri), plus $10 per hour for any time exceeding 40 hours. A.2The baby’s mom will need day care services M-F from 7:30-5:30 (10 hours per day, or 50 hours per week). A.3The baby ...

<Student’s name><Professor’s name><Course number> <The date of the paper>

Part 1. Data collection.

Gather from credible sources the following data:

- The amount of calcium and iron (in milligrams) found in one 10 oz package of broccoli - The amount of calcium and iron (in milligrams) found in a ½ cup of frozen corn - The recommended daily values (in milligrams) of calcium and iron We have found that in 10 oz broccoli there are 116.44 mg of calcium and 2.04 mg of iron. Also we found, that in 1 cup of frozen corn there ...

Before the age of Mohammed Muslims said that their people lived in the age of ignorance and the Arabian Peninsula was an archaic place that housed a myriad of religions and cultures – some sort of political wasteland (Basif, 2013). The Bedouins were the nomads that occupied the peninsula and provided the backbone for the social atmosphere. They were skilled travellers and controlled the commercial networks. While the peninsula housed a lot of towns and cities, Mecca stood out from them all. It was not a major trading city or a crossroad to one but it stood near an oasis marked by a black cube. ...

Karl Theodor Wilhelm Weierstrass was a German mathematician who is often called as the "father of modern analysis".

Weierstrass was interested in the soundness of calculus, and also made significant advancements in the field of calculus of variations. Among the several significant axioms, Weierstrass established a necessary condition for the existence of strong extrema of variational problems. As we know, Cauchy gave a form of the (ε, δ)-definition of limit, in the context of formally defining the derivative, in the 1820s, but did not correctly distinguish between continuity at a point versus uniform continuity on an interval, due to insufficient rigor. Notably, in his 1821 Cours d'analyse, Cauchy gave a famously incorrect proof that the (pointwise) limit of (pointwise) continuous functions was ...

This is a report paper which provides a brief summary of introduction to linear algebra by John R. Durbin. The paper shall provide a brief summary of the three chapters of the book; chapter 11, 12 and thirteen.

Introduction

Modern algebra has been causing much difficulty to the learners and the professors as well. This is attributed to the complexity of the unit and elaborative theorems and formula used in the unit .therefore in this papers I have tried to simplify the theorems and formulas to easen the understanding of the topics such as Galois theorems permutation and many more. This report will ...

Corse title:

1. Using Boolean algebra laws, a negation is denoted by a NOT gate in the circuit. Assume the input signal at X is 1. As it passes the NOT gate it becomes 0. Using Boolean algebra, note that NOT gate is a negation of the input signal, which is 1, hence the output becomes 0. This 0 is the input of the OR gate. This similar to the Y but, at Z the signal is not affected since there is no negation by NOT gate. The truth table for OR is a mathematical representation of Boolean algebra on logics is similar to ...

Introduction

Islam also has a glorious and great history and heritage that has shaped the modern civilization in the West, including culture, education, and scientific developments. Unlike other religions such as Christianity where science and religion form two separate entities, the study of science has always been compatible with Islam religion. One such contribution is found in the field of mathematics where Muhammad bin Moosaa Al-Khawaarizmi is credited as one of remarkable founders of Algebra. He introduced the basic algebraic methods of balancing and reduction, and developed a number of formulas for solving such problems. In such a way, he was able to ...

- Problem Statement – Area(s) of Improvement In any educational process the only way for a student to learn is by actually remembering what they have been taught. This is doubly true in any of the more precise subject such as math, science and technology; all of which rely on solid evidence to prove someone’s point and more importantly, numbers. By this very attribute, math has gained the ire of students around the world despite the numerous improvements and possibilities the field has provided to society. In this light, the main problem that this research paper is ...

Thesis Statement

Algebra is one of the broadest terms used in the field of mathematics with its application in real life situations traceable way back in the ancient Babylonian times over four thousand years ago. The development of algebra was based on finding a solution to solving arithmetic equations mostly in the religious rituals and dilemmas. Most of the renown historical mathematicians such Rene Descartes made some of the major contributions to the development of the modern algebra whereby he came up with la geometre, a publication which focused on improving problem solving techniques in the field of geometry. However, the origin of ...

Introduction

The Hindu-Arabic numerals are said to have come from the Hindus, Egyptians, Persians and Arabs. There is a presumption that the interrelation between traders served in carrying the symbols from one region to another and hence the accumulation from the different origins. Nonetheless, India is said to be the country that first used the largest number of numerals. The numeral system was established in ancient India. Prior to the emergence of Arab Empire the numeral system of the Hindu and Arabs was already going towards the West. The Arabs adopted the nine numerals in the 9th century. Initially, it was ...

Mathematics is a creative and reasoning activity engaging generalization and abstraction to recognize, define and use relationships and pattern. Math’s symbolic nature gives a powerful, concise and precise means of communication. Mathematical concepts have progressed across all humanities from ancient times and are always advancing. It is essential to technological and scientific development in many arenas of endeavor. Moreover, to its applied usage, learning mathematics is a valuable quest in its own right, giving opportunities for challenge, originality, and leisure (Board of Studies NSW, 2012). To learn mathematics, students must be taught with a curriculum or syllabus that gives skills, knowledge, and ...

The scientific revolution of the 17th century is strongly associated with the name of a genius scholar Isaak Newton. His contribution to the world’s scientific thought can hardly be overestimated. Born in 1642 on the Christmas night in Woolsthhorpe, which is situated in Lincolnshire, England, the child was destined to change the world and become the culminating figure in the revolution of scientific knowledge. A genius as he was, Isaak Newton left his legacy in every fundamental area of that time science: mathematics, mechanics, optics and astronomy. Isaak stepped into this world in the farmer’s family ...

According to Stanoyevitch (2010), cryptography refers to one of the oldest branches of pure mathematics that primarily deal with the study of integers. It deals with the prime numbers and also the properties of the objects which are made out of the integers like the algebraic integers. Cryptography is a very important tool for protecting information from unauthorized access in the computer systems. Currently, finite fields are becoming very vital in cryptography. Most cryptographic algorithms depend heavily on the properties of the finite fields especially the elliptic curve cryptography and the Advanced Encryption Standard (AES). The most important concepts of ...

Muhammad ben Musa al-Khwarizmi

Muhammad ben Musa al-Khwarizmi was a Persian astrophysicist, geometrician, and geographer. He was born in Persia at around 780 and died around 850. Though his name signifies that his family was originally from the region around Khwarizmi nearby the Aral Sea, historians trust that al-Khwarizmi was congenital in the town of Baghdad, which the current day Iraq. Though diminutive is identified about his cloistered life, al-Khwarizmi’s effort and participation have principally endured the ages discreetly intact. The exclusion is a volume of mathematics in which the novel cannot be established; there is, though, a Latin rendition of his effort as well ...

Introduction

Pythagoras theorem is named after a Greek mathematician Pythagoras who lived in 475BC. Despite the theorem being named after him, he was not the only ancient person who came up or probably used the theorem because the Babylonians and used it in ancient civilization. In the theorem Pythagoras creates a relationship between the hypotenuse and two sides of a right angled triangle as a2 + b2 = c2. Later on, mathematician from north Europe came up with Pythagoras triples to simplify on ways of obtaining sides of right angled triangles. As years went by, different mathematicians came up with different was of proofing the ...

Personal Portfolio

During my studies at the university I have taken courses in algebra, statistics, English, history, wind energy, and pharmacology. This wide variety of courses has helped prepare me for interdisciplinary studies in that I am creating a wide base and background of basic knowledge in multiple areas. This variety will give me a basis well in the range of areas as they move into upper-level courses and become more specialized in certain areas during my studies in my later years of schooling. The algebra course that I took builds on basic knowledge that is required of high school graduates. These ...

Introduction:

A linear equation is an algebraic equation in which the highest power of the unknown variable is a unit. Linear equation is in the form of where a, b and c are constants and x and y are the variables of the equation (PBS. Mathline). A linear equation produces a straight line graph when plotted to scale on a graph paper.

Solving a System of Linear Equations

A system of equations is the case when we have more than one linear equation. (When there are two or more equations). For elementary studies, the number of unknowns in the system is equal to the number of equations in the system. We ...

Question 1

R { 1,2,3,4 } Z { 5,6,7,8 } F is a subset of RZ Where each element X ∈ R and each element Y ∈ Z (x, y) ∈ F

F subset { y ∈ Z| ( x, y) ∈ F for some x ∈ R}

R is the domain

Z is the codomain

, (4), ∈ Z

2.65 to 6.65

On the graph point 2.65 is (2.65, 4)

And point 6.65 is (6.65, 4) x ∈ Z y ∈ R ( x, y ) ∈ F is a subset of RZ Using = 4 Transforming R along itself

R ( 2.65, 4 )

F( 6.65, 4 ) R + Z defines a function since each element of R occurs only once among the ordered pairs. Where set: R is the ...

The paper analyzes and discusses different concepts related to Algebra. The paper talks

about Order of Operations, Linear equations and their application, linear inequalities,

Quadratic equations. It talks about and summarizes different methods of tackling and

simplifying such algebraic expressions. Finally the paper dwells into different functions and

their graphic representations.

Algebra and Functions

Order of Operations: Order of operations is a mathematical that determines the

correct order for solving any of math operations. Powers and roots are solved before

multiplication and division, which in turn are solved before addition and subtraction

(Toolingu, n.d.). The rule is used in calculation and simplification of a complex algebraic

expression involving many arithmetic operations. Order of operations ...

This discussion post or essay has basically been undertaken to understand some standard

results in Algebra in Mathematics. We would analyze the importance of using derived and

standard results and also about how they ease our calculations drastically. We would also

learn about some elementary but very important terms like Exponents, Integers etc. and

their usage with respect to solving questions in Algebra.

Here in the given questions we have got three variables namely a, b, c which have been

assigned values according to the problem statement (based on my date of birth). All three

variables are integers with ‘b’ being the lowest term and hold the following values:

a= 8 b=-2 c=87

Then we evaluate the algebraic equations based on the values of these three values.

...

Impact of Technology on Supporting First Grade Students’ Creative Thinking in Mathematics

Abstract: This research provides an in-depth examination of the impact of technology in supporting the acquisition of mathematical creative thinking skills among first-grade student. It examines how technology can be properly integrated with mathematics to promote math’s performance without declining creative thinking skills in mathematics among the elementary students. Social constructivism theory as the method of learning in first-grade mathematics students is advocated; it defines the developmental stages of a child and relates to his or her learning and problem-solving ability. Its requirements can properly be integrated to Computer-aided learning processes. The value and importance of ...

Modern American fiction often concerns itself with identity; the individual is often at stake in part of a larger group, whether it be a family, village, or the societies of a big city. Perhaps it is the very nature of American fiction to place identity at the core of much of its short fiction; as a relatively young country that evolved quickly through colonial times and the industrial revolution, its population comes from around the world yet still seeks to define itself as a nation. Therefore, it is no surprise that in the diverse fiction of America, the theme of identity is wrestled with ...

An Exploration of the American Dream as it is presented in Salinger’s “A Perfect Day for Bananafish”, Updike’s “A &P” and Baldwin’s “Sonny’s Blues” The American Dream is often thought of as a defining national characteristic of the USA. The Dream is most frequently thought and spoken of as the opportunity for financial success and material prosperity, achieved through determination and hard work. The three succeeding short stories show the authors’ critical standpoint towards the American dream. To begin with, Seymour Glass in “A Perfect day for Bananafish”, Sonny in “Sonny’s Blues” and ...

Many different themes of apparent opposition come from reading James Baldwin’s classic short story, Sonny’s Blues. There are themes of life versus death, good versus bad, light versus darkness, safety versus danger, white versus black, seeing versus blindness, and outside versus inside, to name only a few. A theme that encompasses all of these supposed oppositions is order versus chaos. The characters in Sonny’s Blues attempt to make order from the roiling dangers of poverty, addiction, war, and other chaotic elements of life in Harlem of the 1950s. However, Baldwin does not present chaos and order as ...

Summary

Bilal Haq, a scientist from the National Science Foundation Arlingtion, Virginia encountered foraminifera on his trip to Qingdao in China. Foraminifera are small creatures that grow shells on their bodies. Their shells are varied and very diverse, as if they are created by visionary artists. Haq thought the foraminifera would make beautiful pieces of art and should be put on display. Haq’s fellow colleague from China, Zheng, agreed and put things into action by involving local craft workers. It resulted in a park for foraminifera since the end of 2009 and already a million people have visited (Larkins, 2012).

It is ...

The science of numbers otherwise known as mathematics is various disciplines and principles that involve changes in structure, space, quantity and change. It has been a fundamental of many other sciences that rely on numbers for reasoning. Being said that, mathematics need to have learning standards. Because having standards in mathematical learning will give students realistic and clear expectations of what they are about to learn in math disciplines. Students will also have understanding of the reasons why learning math is detrimental in connecting concepts to their previous learning and how they apply in practical situations.

How do standards improve ...